Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3"Â and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Engaging Students in Their Learning

5 minutes

Inclusion is a way to make connections between students past and present learning. It is also the Engage in the 5 E's of Engage, Explore, Explain, Elaborate and Evaluate. This is when I focus students' thinking on the learning outcomes of the content we will be working with.

My students' day begins when I greet them at the door, as I would a guest into my home. They enter the room and get themselves settled in while I finish greeting everyone. Once settled, students copy the agenda into an Teacher Agenda.JPG/Key Point Journal. The purpose of the agenda is to make a clear and specific statement of my intentions for the day. It is like a mind map of the day. It also helps teach time managements skills.

Once the Agenda is copied I have my students join me in a community circle on the floor. You can see examples of student agendas here. Student Agenda 1 and Student Agenda 2.

I start today's topic with, "How would you persevere in completing a large number of simple math problems?" I toss the koosh ball to one student and they say, "I make myself keep going because I want to do all the work." This student tosses the koosh to another student who answers, "I will work with a friend to keep going and check our answers against each other." The next reports, "I will take a break, getting a drink and then go back to work."

This continues until about ten students have offered an answer. I then ask, "What did you notice that was a common answer?" The student who has the koosh last tosses to another student, because they know that the purpose of tossing the koosh is to include as many different students as possible.

There is a consensus that perseverance will be needed to finish all the problems. I agree with this conclusion and send them back to their seats with the question, "What is a palindrome?" I hear my 5th graders start to talk, saying things like "race car" is a palindrome. It is the same frontwards and backwards. This activated my 5th graders prior knowledge and their knowledge that it is a classroom expectation that they, in turn, introduce the new word to my 4th graders.

This part of the activity started under the Explain of the 5 E's. I gave the students the definition of palindromes and some examples. I did this by writing the definition and examples on a lined piece of paper under my document camera. This gives me the opportunity to model how I want students to take notes in their math journals.

Student Agenda 1

Student Agenda 2

Teacher Agenda

Palindrome - Student Work Example

Exploring Palindromes

I continue to write at the same time my students are copying because I know I have a tendency to go too fast and I want to slow myself down. I also have a signal in my class of students raising their hands and letting me know they need more time. If some are not keeping up - which happens a lot at the beginning of the year - I ask if they have the definition copied down and remind them that they don't have to have all the examples I am putting up.

When I start to put the examples up I know they are about to really get excited because they really understand a palindrome is the same frontwards and backwards, and the examples are silly. I slow down because I know this excitement will carry through to all the math problems they will be doing in the next couple of minutes.

My next comment to my class is, "Are you curious about how you can find a palindrome for every number?" I let them talk in their groups for under a minute. This lets them get their excitement out as well as share ideas with each other.

I get their attention again by ringing the chimes. My students know this is a signal means they can finish their sentence and then look to me to show they are paying attention again.

I go on to show them if they take a double digit number, reverse it and add it to itself you can get a palindrome. Sometimes it takes more than one step but that is the fun of it.

We popcorn a review of how our classroom agreements will look/sound and feel like in this activity. I do this because I am about to let them sit anywhere in the room to do the work and this helps remind the students about our classroom expectations. While we are tossing the koosh I pass out the Palindrome Recording Chart - and tell them they are about to work hard and persevere in solving all the palindromes from the numbers 10 - 100.

Once this is done and I have gained the students attention again - raising my hand - I walk them through how to record their answers and explain that they will not be able to "do the math" on their handouts - their journals would be a better place. I reinforce at this time they need to be sharing their answers to their math problems. What if you are on step 6 of a 10 step problem and you made a mistake on step 3? That is a lot of time spent on a problem with a mistake in it.

The first Student Led (Video 1) is an example of how my students gather together and work to finish a large assignment. In this video there are an equal number of 4th graders and 5th graders working together. It is a 5th grade boy who has taken leadership of organizing the work. This is typical for the first few weeks of school in my multiage classroom. My 5th graders have already been with me for a year as 4th graders. They know my procedures and expectations and love to share this with the newer 4th graders. This allows an opportunity for my 5th graders to be positive leaders. Even if they struggle in math, they can be successful in this lesson because the math is a review of multi-digit addition for them.

Video 2 shows how I differentiate with students work habits. There are students working alone or small groups. They are sitting on the floor and at tables. With this lesson I have set my students up for success in the beginning of the year and positive behavior expectations.

Student Reflection

5 minutes

I use reflection questions to guide student evaluation of their learning on concepts, skills and behavior. I am also able to evaluate their learning from this. For this activity I want to focus on how the students were able to accurately complete many math problems using a repeating pattern. The questions I used were:

1. How did you persevere and make meaning of the math?

2. If you made a mistake how did you find and correct it?

3. Did you work with a partner? How did this help?

You could ask your students these questions verbally or have them written down on a board, large poster or Power Point. Another idea would to be type them out and copy the paper for each student.

When I notice students finishing their writing of their answers in their math journals I start a reflection discussion. Popcorn sharing their answers to each question keeping to three-five students for each question. I find it important for the students to share out a lot at the beginning of the year to help extend each others thinking and reinforce positive behavior. The questions I ask during this discussion guide the students to more complex thinking skills - "How did you know that?" "Why did you do it that way?"

Not all students will be able to finish all of the problems but there are some who problem solve and find a partner to "divide and conquer" I make a point of sharing this with the class. I also complement the students who I know work the entire time. I don't want them to be discouraged but to celebrate working to their personal best.